This highly readable volume on optimization in function spaces is based on author Amol Sasane's lecture notes, which he developed over several years while teaching a course for third-year undergraduates at the London School of Economics. The classroom-tested text is written in an informal but precise style that emphasizes clarity and detail, taking students step by step through each subject. Numerous examples throughout the text clarify methods, and a substantial number of exercises provide reinforcement. Detailed solutions to all of the exercises make this book ideal for self-study. The topics are relevant to students in engineering and economics as well as mathematics majors. Prerequisites include multivariable calculus and basic linear algebra. The necessary background in differential equations and elementary functional analysis is developed within the text, offering students a self-contained treatment.